CONVERGENCE OF THE GALERKIN METHOD IN THE ELECTROMAGNETIC WAVES DIFFRACTION PROBLEM ON A SYSTEM OF ARBITRARY LOCATED BODIES AND SCREENS

Smirnov Yuriy Gennad'evich, Doctor of physical and mathematical sciences, professor, head of sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Moskaleva Marina Aleksandrovna, Junior researcher, Research Center “Supercomputer modeling in electrodynamics”, Penza State University (40 Krasnaya street, Penza, Russia), m.a.moskaleva1@gmail.com

517.3

10.21685/2072-3040-2016-2-7

Background. Mathematical modeling of electromagnetic waves diffraction on screen and bodies of various forms is an important aspect in modern electrodynamics. The objective of this work is to prove the convergence of the Galerkin method for solving the electromagnetic waves diffraction problem on a system of arbitrary located bodies and screens.
Material and methods. The statement of the electromagnetic waves diffraction problem on the system of bodies and screens of irregular shapes is considered. The stated problem of diffraction is presented as a system of integral-differential equations; properties of the system are studied using pseudodifferential calculus in Sobolev spaces.
Results. The problem of diffraction is formulated; the boundary value problem is reduced to a system of integral-differential equations. To solve the system the authors suggest the numerical method of Galerkin with finite basis functions. The convergence of the Galerkin method is proved.
Conclusions. The results of convergence of the Galerkin method for a system consisting of a plane screen and inhomogeneous anisotropic body are obtaned; they are important for further theoretical and numerical studies of the problem.

diffraction problem, system of integral-differential equations, the Galerkin method, the basis functions, elliptic operator.

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